Macroscale analogues^1,2,3 of microscopic spin systems offer direct insights into fundamental physical principles, thereby advancing our understanding of synchronization phenomena⁴ and informing the design of novel classes of chiral metamaterials^5,6,7. Here we introduce hydrodynamic spin lattices (HSLs) of ‘walking’ droplets as a class of active spin systems with particle–wave coupling. HSLs reveal various non-equilibrium symmetry-breaking phenomena, including transitions from antiferromagnetic to ferromagnetic order that can be controlled by varying the lattice geometry and system rotation⁸. Theoretical predictions based on a generalized Kuramoto model⁴ derived from first principles rationalize our experimental observations, establishing HSLs as a versatile platform for exploring active phase oscillator dynamics. The tunability of HSLs suggests exciting directions for future research, from active spin–wave dynamics to hydrodynamic analogue computation and droplet-based topological insulators.

微观自旋系统的宏观类似物^1,2,3提供了对基本物理原理的直接洞察，从而促进了我们对同步现象⁴的理解，并为新型手性超材料^5,6,7的设计提供了信息。在这里，我们将“行走”液滴的流体动力学自旋晶格 (HSL) 作为一类具有粒子波耦合的主动自旋系统引入。HSL 揭示了各种非平衡对称性破缺现象，包括从反铁磁到铁磁有序的转变，这可以通过改变晶格几何形状和系统旋转⁸来控制。基于广义 Kuramoto 模型^{4的理论预测}源自第一性原理的研究使我们的实验观察合理化，将 HSL 建立为探索有源相位振荡器动力学的多功能平台。HSL 的可调性为未来的研究指明了令人兴奋的方向，从主动自旋波动力学到流体动力学模拟计算和基于液滴的拓扑绝缘体。